Animation Node Grid Animation
First you may try the Delay Falloff node, it will rely on the order of the objects.



If the order of the objects is not what you want, you may consider using the Selection Order ID Key Method:



Check the Documentation for other ordering methods.

And of course you can sort objects using the Sort List node, and sort objects by name:



Or based on the object's y location.



Or in a slightly more complicated method, by using the formula e.location.y + (e.location.x)/1e5 Which will make the animation start from the left instead of the right. Which is exactly what you want I suppose.



Exact solution to your problem:



Lets say your grid is composed of n objects, you instance the cube 2n times, n cube for the right one and n cube for the right one, so 2n in total. Then you edit the first n objects as you wish in whichever method you like, then you offset the final vectors couple of units in the required direction and then combine both the unoffsetted and offsetted vectors and transform the objects based on them.